000 03927nam a22005415i 4500
001 978-981-97-2624-0
003 DE-He213
005 20251030112614.0
007 cr nn 008mamaa
008 240704s2024 si | s |||| 0|eng d
020 _a9789819726240
_9978-981-97-2624-0
024 7 _a10.1007/978-981-97-2624-0
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
100 1 _aSkibsted, Erik.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980049
245 1 0 _aSpectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds
_h[electronic resource] /
_cby Erik Skibsted, Xue Ping Wang.
250 _a1st ed. 2024.
264 1 _aSingapore :
_bSpringer Nature Singapore :
_bImprint: Springer,
_c2024.
300 _aIX, 258 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematical Physics Studies,
_x2352-3905
505 0 _aIntroduction -- Many-Body Schrödinger Operators, Conditions and Notation -- Reduction to a One-Body Problem -- Spectral Analysis of H0 near 0 -- Rellich-Type Theorems -- Resolvent Asymptotics near a Two-Cluster Threshold -- Elastic Scattering at a Threshold -- Non-Transmission at a Threshold for Physical Models -- Threshold Behaviour of Cross-Sections in Atom–Ion Scattering.
520 _aThis book provides a systematic study of spectral and scattering theory for many-body Schrödinger operators at two-cluster thresholds. While the two-body problem (reduced after separation of the centre of mass motion to a one-body problem at zero energy) is a well-studied subject, the literature on many-body threshold problems is sparse. However, the authors’ analysis covers for example the system of three particles interacting by Coulomb potentials and restricted to a small energy region to the right of a fixed nonzero two-body eigenvalue. In general, the authors address the question: How do scattering quantities for the many-body atomic and molecular models behave within the limit when the total energy approaches a fixed two-cluster threshold? This includes mapping properties and singularities of the limiting scattering matrix, asymptotics of the total scattering cross section, and absence of transmission from one channel to another in the small inter-cluster kinetic energy region. The authors’ principal tools are the Feshbach–Grushin dimension reduction method and spectral analysis based on a certain Mourre estimate. Additional topics of independent interest are the limiting absorption principle, micro-local resolvent estimates, Rellich- and Sommerfeld-type theorems and asymptotics of the limiting resolvents at thresholds. The mathematical physics field under study is very rich, and there are many open problems, several of them stated explicitly in the book for the interested reader. .
650 0 _aMathematical physics.
650 0 _aFunctional analysis.
650 1 4 _aMathematical Physics.
650 2 4 _aFunctional Analysis.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_965563
700 1 _aWang, Xue Ping.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980050
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9789819726233
776 0 8 _iPrinted edition:
_z9789819726257
776 0 8 _iPrinted edition:
_z9789819726264
830 0 _aMathematical Physics Studies,
_x2352-3905
_972779
856 4 0 _uhttps://doi.org/10.1007/978-981-97-2624-0
912 _aZDB-2-PHA
912 _aZDB-2-SXP
999 _c61352
_d61352